Linear stability of confined flow around a 180-degree sharp bend
This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronou...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English English |
| Published: |
Cambridge University Press
2017
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/79094/ http://irep.iium.edu.my/79094/1/SapardiHussamPotheratSheard_JFM2017.pdf http://irep.iium.edu.my/79094/13/79094%20Linear%20stability%20of%20confined%20flow%20%20SCOPUS.pdf |
| Summary: | This study seeks to characterise the breakdown of the steady two-dimensional solution
in the flow around a 180-degree sharp bend to infinitesimal three-dimensional
disturbances using a linear stability analysis. The stability analysis predicts that
three-dimensional transition is via a synchronous instability of the steady flows.
A highly accurate global linear stability analysis of the flow was conducted with
Reynolds number Re < 1150 and bend opening ratio (ratio of bend width to inlet
height) 0.26β 65. This range of Re and β captures both steady-state two-dimensional
flow solutions and the inception of unsteady two-dimensional flow. For 0.2 6 β 6 1,
the two-dimensional base flow transitions from steady to unsteady at higher Reynolds
number as β increases. The stability analysis shows that at the onset of instability,
the base flow becomes three-dimensionally unstable in two different modes, namely
a spanwise oscillating mode for β = 0.2 and a spanwise synchronous mode for
β > 0.3. The critical Reynolds number and the spanwise wavelength of perturbations
increase as β increases. For 1 < β 6 2 both the critical Reynolds number for onset
of unsteadiness and the spanwise wavelength decrease as β increases. Finally, for
2 < β 6 5, the critical Reynolds number and spanwise wavelength remain almost
constant. The linear stability analysis also shows that the base flow becomes unstable
to different three-dimensional modes depending on the opening ratio. The modes are
found to be localised near the reattachment point of the first recirculation bubble |
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